How should I label the classes in RNA?
From a purely dataset-development perspective I would just label the classes with numbers starting from 0 (ID of the first person) to N (ID of the last person.

During training however, what you do with those classes will vary depending on the type of architecture you are training.  For example, if you are building a neural-network classifier you could simply have multiple output nodes.  When running backprop with a label for the ith person you could put a 1 on the ith output layer and -1 on the rest of them.  This is similar to this answer as well

Whatever you end up doing, try not to label your data to the benefit of the algorithm you're trying to run unless you really know what you're doing.  You don't want to accidentally lose information or make your training data less interpretable and harder to deal with in the long run.